One of the most productive approaches to the calculations of knot polynomials (as well as Wilson-loop averages of the Chern-Simons theory, which are equal to them) is modern Reshetikhin-Turaev approach [1]}-[2]}. It is most clearly defined for the braid representation of a knot (see Fig.REF ). Then in such a braid all crossings correspond to \(\mathcal {R}\) -matrices. These \(\mathcal {R}\) -matrices are very simple in their diagonal form. Eigenvalues of the \(\mathcal {R}\) -matrices correspond to irreducible representations in a tensor product of the representations corresponding to two crossing strands. For the knot case and representation \(Q\)  from the product of two representations \(T\)  the eigenvalue is equal to [3]}, [4]}, [5]}, [6]}
\(\lambda _Q=q^{\varkappa _Q-4\varkappa _T-N|T|},\) 
